Brady has only had two "terrible" games which were followed by a bye week before his next game. Here they were:
2001 - week 16, he went 17-29 (58.6%), 198 yds, 1 td, 2 int, 62.1 rating against the Panthers. They earned a bye for the playoffs as the #2 seed, then hosted the Raiders in the Snow Bowl game. For that game, Brady had this line: 32-52 (61.5%), 312 yds, 0 td, 1 int, 70.4 rating.
2002 - week 6, he put up this line in a 28-10 loss to the Packers: 24-44 (54.5%), 183 yds, 1 td, 3 int, 44.0 rating. They had a bye for week 7, then they lost to Denver in week 8, 24-16, with Brady putting up this line: 15-29 (51.7%), 130 yds, 1 td, 0 int, 75.4 rating.
In 2007 he had a "bad" game in the AFCCG against SD in a 21-12 win: 22-33 (66.7%), 209 yds, 2 td, 3 int, 66.4 rating. They had the bye then played the Giants in the SB, where Brady put up this line: 29-48 (60.4%), 266 yds, 1 td, 0 int, 82.5 rating.
Here are all of Brady's stat lines the week after a bye. I'll designate which games followed anything less than a "good" performance, according to my rubric (marked with an *):
2001 - Divisional Round - 32-52 (61.5%), 312 yds, 0 td, 1 int, 70.4 rating - beat Oak 16-13*
2001 - Super Bowl - 16-27 (59.3%), 145 yds, 1 td, 0 int, 86.2 rating - beat StL 20-17
2002 - Week 8 - 15-29 (51.7%), 130 yds, 1 td, 0 int, 75.4 rating - lost to Den 24-16*
2003 - Week 10 - 15-34 (44.1%), 212 yds, 0 td, 0 int, 64.8 rating - beat Dal 12-0
2003 - Divisional Round - 21-41 (51.2%), 201 yds, 1 td, 0 int, 73.3 rating - beat Ten 17-14
2003 - Super Bowl - 32-48 (66.7%), 354 yds, 3 td, 1 int, 100.5 rating - beat Car 32-29*
2004 - Week 3 - 17-30 (56.7%), 298 yds, 2 td, 0 int, 112.9 rating - beat Buf 31-17*
2004 - Super Bowl - 23-33 (69.7%), 236 yds, 2 td, 0 int, 110.2 rating - beat Phi 24-21
2005 - Week 7 - 14-21 (66.7%), 199 yds, 1 td, 0 int, 113.0 rating - beat Buf 21-16*
2006 - Week 6 - 18-27 (66.7%), 195 yds, 2 td, 0 int, 112.4 rating - beat Buf 28-6
2007 - Week 10 - 31-39 (79.5%), 373 yds, 5 td, 0 int, 146.1 rating - beat Buf 56-10
2007 - Divisional Round - 26-28 (92.9%), 262 yds, 3 td, 0 int, 141.4 rating - beat Jax 31-20
2007 - Super Bowl - 29-48 (60.4%), 266 yds, 1 td, 0 int, 82.5 rating - lost to NYG 17-14*
2008 - N/A
2009 - Week 8 - 25-37 (67.6%), 332 yds, 1 td, 1 int, 93.5 rating - beat Mia 27-17
2010 - Week 5 - 27-44 (61.4%), 292 yds, 1 td, 2 int, 69.5 rating - beat Bal 23-20
2010 - Divisional Round - 29-45 (64.4%), 299 yds, 2 td, 1 int, 89.0 rating - lost to NYJ 28-21
2011 - Week 7 - 24-35 (68.6%), 198 yds, 2 td, 0 int, 101.8 rating - lost to Pit 25-17
2011 - Divisional Round - 26-34 (76.5%), 363 yds, 6 td, 1 int, 137.6 rating - beat Den 45-10
That's 18 games following a bye. Of these 18, here's where they would fit in my rubric:
excellent: 3 (16.7%)
very good: 6 (33.3%)
good: 3 (16.7%)
average: 2 (11.1%)
poor: 3 (16.7%)
terrible: 1 (5.6%)
So 12 of the 18 (66.7%) were "good" or better.
Of these 18, just 6 of them followed a performance that was "average" or worse. Here were the QB ratings in those 6 instances: 70.4, 75.4, 100.5, 112.9, 113.0, and 82.5.
So again, a bit of a mixed bag. He's never been hideous in that situation, but he's never been insanely brilliant either. He's either been below average or very good. 50-50 proposition, really.
Wish I had better news to share!